Toric spectacle lens



A. GLEICHEN. TORIC SPECTACLE LENS. APPLICATION FILED APR. 5, 1921.

Patented De c. 12,1922.

Inveninr:

Patented Dec. 12, 1922.,

\ Uhilithh inane earner os ALEXANDER GERMANY. i i

memo sPnc'rAoLn LENS.

Application filed April 5, 1921. Serial no; 458,869.

T 0 all whom it may concern:

Be it known that I, Dr. ALEXANDER GLEICI-IEN, citizen of the German Republic, residing at Berlin, Germany, have invented certain new and useful Improvements in Toric Spectacle Lenses (for which applications have been filed for Letters Patent in the following countries: Germany, tiled March 17, 1919; France, tiled June 19, 1920; Italy, filed June 23, 1920; Great Britain, filed June 23, 1920; Japan, filed August 28, 1920), of which the following is a specification.

This invention relates to toric spectacle lenses of the kind with two planes of sym metry and to'lenses with two toric surfaces as well as to lenses with one spherical and one toric surface.

l l hen by means of such a lens an astigniatic eye is fully corrected along the optical axis, a rcduction'in. the sharpness of vision is nevertheless generally noticeable in oblique directions with the eye rolling. This results in the appearance of dispersion or divergence figures on the retina, which are formed by the injurious astigmatism of the pencils oi rays retracted with a strong inclination to the axis. it clear and satisfactory vision is allected not only by the oi. the said dispersion or divergence figures, but also by the diiierent sh 1 oi the same in the 1neridlocal section and in the'equatorial section of the lens. lVhen th shape considerably differs in the two tions, the eye will find different conditions of vision changing very quickly and will itseli': const .itly to these changing conditions. In order to avoid as much as possible this expenditure of energy which is very bad tor the eye, the small degree of the dimness in the two main sections which cannot be completely eliminated, is made, according to this invention. oi uniform character.

As will be described hereinafter, this is attained by arranging that for pencils of: rays oi medium inclination which intersect each other in the same point of the axis about mm. behind the apex of the lens on the eye side and of which one pencil travels in the meridional s rcction. and the other in the equatorial se tion. the circles of least contusien are situated on a sphere which is drawn about the above mentioned point of intersection oi? the main rays.

figures 1 and 2 each show the path oi. a

myopia be torced to adapt pencil of rays in a vertical plane through a toric lens which is assumed to co-incide with the meridional section through said lens, Fig. 1 showing; the path of a pencil the axis of which is co-incidinp; with the axis of the GLEIGI-IEN, or BERLIN, GERMANY, assrenon To meme orrrscns lens, whereas Fig. shows a pencil with oblique incidence. The equatorial section throughthe lens is assumed to be a horizontal section through the lens when in operative position before a human eye, said equatorial section being at right anglesto the vertical section. and to the plane of the paper of the drawing.

The refractive powers or apex ice-fractions have the values D and D in these two sections, the indexes v and h standing for the words.vertical, and horizontal? The two foci E. and F are accordinglysituated in the optical axis. v i i Figure lshows the path of the rays in a toric glass with negative apex refractions, such as are used therefore for correctingor short sight, together withthe human eye; and'by way of example it is assumed that it is. question of a lens for viewing); distant objects. I 4

The lens itself is shown diagrammatically in vertical section and marked G. ltsapex' at the e e side is E. The point Z is assumed to represent the centre of rotation of the eye. It a pencil of rays parallel to the axis (not shown in the figure) strikes the lens, it will be retracted, and will strike the pupil A of the eye (or strictly speaking the entrance-pupil of the eye). In this way the pencil is given at this point a circular cross-section with the centre R.

As is well known, the pencil is soreitracted as to produce a virtual Sturms conoid, with the toci F and F for the vertical and the horizontal. section. All the rays of the pencil pass, as is known, through two foci situated at E, and F3, which are at right angles both to the optical axis and to each other; As is well known, the cross-sections ofthe Sturm pencil, apart from those at the foci mentioned. are generally ellipses (for instance L in Fig.1) at onepoint between the two foci there is however a circular cross-section with theccntre at K in Fig. 1, which described in the literature oiv the art as the circle of smallest confusion. A cross-section of the pencil is the already mentioned pupil of the eye with the centre ll.

. From the well. known properties of Fltnrms second circular ice conoid it can be easily deduced that the two astigmatic foci and the centres of the two circular pencil. cross-sections, and therefore the four points F F ,,,R, and K are four harmonio points,a propositionwhich, as can be easily proved, applies generally to every infinitelythin 'asti matic pencil of rays.

I r 1 1 2 f 2 i I -When the toric lens in question is the cor-- 'rectingdistant lens of the astigmatic eye, the

points 11, and R, must, as is well known, co-

, incide with-the astigmatic far poi'nts of the eye, so that R and F are conjugatedwith the retina point, relatively to therefracting system of the astigmatic eye, in which the opticalaxis intersects the retina. I 1 When the/ eye rolls about the centre Z situated about 10 mm. behind R, the points "F and F11 willcachdescribe a spherical surface whichis described as the astiginatic In the same. way, the

point Z, and their radii are ZF ZF and ZK.

Asthe axis ofthe eye now assumes an oblique position relatively to the optical axis of the lens, thepencils of rays arriving in the eye, no longer travel in the. direction of the optical axis ofthe toric lens, but pass through the latter in an oblique direction.

I The form. of the astigmatic pencils produced thereby, deviates, it is true, from the Sturms cono'id, in as far as the ray combinationin the meridional and sagittal pencil components areno longer of the same magnitude, and the astigmatic focal lines are no longer both at right angles to the axis of the pencil, butas regards the'shape of the cross-section the conditions are quite simi lar to thoseintheiSturms conoid.

Of the various pencils which during the rollingof the eye, can pass into "the pupil,

there will first .be examined only those which, on'the one hand-in verticalsection,

and onthe other hand in horizontal section,

travel at an average angle of about 30 to theaxis, andintersect each other at thesame pointof the axis Z about 25 mm. behind the apex; oflthe lens on the eye side.

These two pairs of pencils will be in the following referred to shortly as oblique pencils? If such a virtually astigmatic pencil of rays coiningout ofthe toric lens is considered, the two astigniaticcfar points will be situated on the same, namely at the point where the pencil axis intersects the. two i'ar point spheres. But the foci of the virtual pencil will'not now coincide exactly with these fanpcints, as. the pencils pass ing through the spectacle lens in oblique direction will have an injurious astigmatism.

' dence'in vertical section. I If therefore" F :p v1 3:32 KRz then there'will be the relation:

Here again F F Z is the optical axis of the toxic lens G which however is only diagrammatically indicated in vertical secl tion. The centre R of the pupil of the eye 7 F and F which correspond to the points F and F on the optical axis. Let the meridional and sagittal focus of the pencil be represented by the points T and S. If these coincided with the points F and F the astigmatism on the oblique pencil would be equal to that on the optical axis, and no reduction of the sharpness of vision would take place. As however these points do not coincide, the F sphere will be intersected at F by the meridional pencil portion comingfrom the edge points; 1 and 2 of the pupil in a dispersion ordivergent line, the lengthof which will be called in where therefore the index t refers to the meridional pencil portion, and the index v to the fact that it belongs to the vertical. sectron. In asnnilar way, the sagittal P611011,

portion coming. from the points 3'and 4 will intersect at F the R. sphere in a dis persion or divergent line which will be called 1 Making in Fig. 2

TR- zt sn z and as before ov o v f pv F and designating the diameter of the pupil, 110 to be considered as being circular, by Zr there exists a simple proportion:

' i l l (3) je Zl I 2 h 0v Similar considerations could be made for the pencils traveling in the horizontal sec- 3 tion. Using the index h in order to indicate that it belongs tothe horizontalsection, there is for the meridional portion the relation:

hlih ent Zro'i ph ,P oll and for the sagittal portion:

v e e and a represent the angles at which the dispersion or divergent lines 1 1 t, 1 and 1 are seen from thec entre ofthe pupil of the eye. As these dispersion lines are situated on the astigmaticflfar pointspheres, that is to say are conjugated with the point of retina fovea), they can be reproduced sharply on the retina. c y

In View of the comparatively small focal distances of the eye, whichal'so in the astig matic main sections deviate from each other only comparatively little, and in view of the fact that the retina is always situated comparatively close to the focal plane ofthe eye, the corresponding retina images may be taken as being proportional to the said angles a a e and a and as the proportionality constant can be usedinv the first approximation the average value of the front focal distance of the diagrammatic eye which is called f Designating the retina images of the above mentioned dispersion lines for the pencil in the vertical section withwlr and zl/ and for'the'pencil in the horizontallsection p. and ,u then l t fo tv la s fo sv i I s -fo sh l 't fo th I The values gb and 1l/ canbe therefore con-i sideredas the two axesof the generally ellip tical dispersion circle on the retina, which is produced by ithe pencil travelling in the vertical section. The values a and v i have analogous meaningi'or the pencil in the horizontal section: From the equations 2 to 6, it follows:

rails. ov Pv Ph 1 1 l 1 In a toric spectacle lenswhen it is limited by two toric surfaces, there are available first four different radii as constructional elements, as the thickness'of the lens need not be considered asan eiiicacious'means' torcorincting the path of rays. As however tree constructional element remains available.

The dispersion circles on the retina for the obliquely tailing pencils" oi -rays' cannot bemade to'disappear by means of a toric The condition for theysame is t=s and l s=l t or,in accordance with the equations 7 and 8,

an'clwith due regardto the equation 1 It thedistance otthe circleot smallest contusion from the centre R of the pupil in the oblique pencilsot the vertical and horizontal sections .is designated respectively with p and p then in accordance withthe above mentioned proposition, for

lens, for this would necessitate that the tour ,astigmatic pencil penetrating into the eye,

the centre of the circle otsmallest confusion, the centre of the pupil andthe ast gmatic image points are harmonic points From the latter equations follows:

(12) p p The condition required in order that the dispersion figures oi? the corresponding oblique pencils on the retina should be circles, is that the centres of the circles of 11). Pub p,

' smallest confusion of the axis. pencil andot each flO

the oblique pencils, should be situated on one and the same sphere, the centre of which s tllfiPOlIil'fiOf 'lIltQlSGClDlOIl of the main rays (centre'of rotation of the eye). i y "Asinthe present case'only two conditions have to -be-fulfilled, this can be doneqby meansof atoric lens, bothffaces of which arextoric surfaces. I a

In practicechowever. toric lenses with one spheric surface the so-called tro-spheric or sphero-toric glasses, o are ofv special impel tance' but in their case as already stat-ed,

only a single free constructional element is available.

Itis true that in this case it is no longer possible to make the dispersionfigur'es circular 1n accordance with the equations? and 8 asthls would're uire twoco'nditlons to be fulfilled; but in the two; oblique pencils the deviation from the circular shape, which is.

expressed bythedifference of the transverse diameters of the dispersion fignres, namely by thevalues :,b 'J/ and a ean be made equal to each other. In tlllSKpfiLSG- ness in the two 0 lique pencils, the centres of the dispersioncircles of the said two pencils must be therefore situated on a sphere, the

centre of whichfisin the point of intersectlon of the main rays (centre of rotation of the eye).

It goes without saying that theresults obtainedare valid also for posltive lensesjwith real astigmatic image points.

It must be further pointed outthat in w.

cordance with the usual definition, the sharpness, of visionis in the inverse ratio to the physiological limit angle when thelatt'er is expressed inangle minutes. In the present case; howei er the angles a e afe aiid fe are identical with the said limit, angles;

their reciprocal values supply therefore di rect a measure for the sharpness of vision in the meridional and sagittal portion of the two oblique pencils.

In the following is given by way of example a construction, namely for a negative toro-spheric lens. The frontiradii of the torus in the vertical and horizontal section are marked he and r and the rear radius of thesphere with a" As the measure of length is used the meter, The refractive index .is 4221.52, The point of intersection of the, -1nainrays is 0,025 in...behind-the lens I apex at the sideof the eye. Further D 8 dptr. D 4 dptr.

7111 010613 V FQ-Q 5 ThicknessdIQOOL o are all taken in the following as being positive. With an inclinationof the main-rays. at theflside of the eye ofBQ", i

v s osoifiso I i I toh 0-26950 r i U I p oh oh 0.139162 s o in accordance with the equation 11,

' The centres of thecircles of smallest confusion are therefore situated practically on one and the same sphere drawn about the point Z, for the difference of their dis- The sections or lengths shown inFig. 2,

tanc esv from the point Z amountsonly to i I e s oooo om Further the syalues in angular seconds willbe a 374", av 3524'; e zse", 's 52" which as already stated are in inverse ratio to the sharpness of vision in the pencil coinponents in question. These sharpnesses of vision themselves would be obtained by dividing the figure 60 by theabove figures for 's as lis and 5 These valueslead to a more favorable result than is the case withn'vell known lenses of thesameaxial refractive powers; more particularly the extraordinarily favorable correction must: be mentioned in the specially important horizontal section in which the sharpness of vision still considerably exceeds the unit.

What Iclaimisi i l j ,1; Aspectacle lens with at least-one toric surface and two planes of symmetry havingsuch radii of curvature that the circle of least confusion for a pencil of mean 013-.

liquity in one 'of said planesrof symmetry which intersects the axis of the lens at a,

distance of about 25 mm. behind the lens has the same distance from this point of intersection as the circle of least confusion of a pencil which at the same obliquity as that of the first named pencil is passing in the second plane of symmetryand intersects the axis likewise at the above mentioned point.

2. A spectacle lens with two toric surfaces and two planes of symmetry having such radii of curvature that the circle of least confusion for a pencil of mean obliquity in one of said planes of symmetry which intersects the axis of the lens at a distance of about 25 mm. behind the lens has the same distance from this point of intersection as the circle of least confusion of a penoil which at the same obliquity as that of the first named pencil is passing in the second plane of symmetry and intersects the axis likewise at the above mentioned point,

the axis of the lens from the said point lying about 25 mm. behind the lens. I

In testimony whereof I have signed this specification in the presence of two subscribing witnesses.

DR. ALEXANDER GLEIGHEN. Witnesses:

MAX FAsHNER, 'JAK BERNATH. 

